It is well known that the successive balancing numbers are relatively prime. Let for all integers a, sn(a) denotes the greatest common divisor of the shifted balancing numbers of the form sn(a) = gcd(Bn a; Bn+1 6a).In this study, we will show that fsn(1)g is unbounded whereas fsn(a)g isbounded for a 6= 1.
@article{26093,
title = {Greatest common divisors of shifted balancing numbers},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {35},
year = {2016},
doi = {10.5269/bspm.v35i3.26093},
language = {EN},
url = {http://dml.mathdoc.fr/item/26093}
}
Ray, Prasanta Kumar. Greatest common divisors of shifted balancing numbers. Boletim da Sociedade Paranaense de Matemática, Tome 35 (2016) . doi : 10.5269/bspm.v35i3.26093. http://gdmltest.u-ga.fr/item/26093/